• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.239-261
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• 2008

This study presents results by the content areas in mathematics. Average performance is provided for five content areas: number, algebra, measurement, geometry, and data. Relative achievement is shown among the content areas for 4 countries in comparison to Korea. In number, Korea had lower average achievement than Singapore, especially for ratio proportion percent. Among 5 countries, Korea had the highest average achievement in algebra and geometry, but the lowest in attributes and units of measurement. In data, Korean students didn't learn the followings successfully: a) comparing characteristics of data sets and using mean, median, range, and shape of distribution, b) interpreting data sets (e.g., draw conclusions, make predictions, and estimate values between and beyond given data points), c) evaluating interpretations of data with respect to correctness and completeness of interpretation.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.1-22
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• 2017

This study investigated three $10^{th}$ grade students' concept of rate of change while they perceived changing values of given functions. We have conducted a teaching experiment consisting of 6 teaching episodes on how the students understood and expressed changing values of functions on certain intervals in accordance with the concept of rate of change. The result showed that the students did use the same word of 'rate of change' in their analysis of functions, but their understanding and expression of the word varied, which turned out to have diverse perceptions with regard to average rate of change. To consider these differences as qualitatively different levels might need further research, but we expect that this research will serve as a foundational study for further research in students' learning 'differential calculus' from the perspective of rate of change.

• East Asian mathematical journal
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• v.39 no.4
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• pp.479-492
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• 2023

Although Euclidean plane geometry is implemented in the middle school course, there are three major problems in high school space geometry that can be intuitively taken for granted or misinterpreted as circular arguments. In order to solve this problem, this study proved three major problems using sets, Euclidean plane geometry, and parallel line postulates. This corresponds to a logical sequence and has mathematical and mathematical educational values. Furthermore, it will be possible to configure spatial geometry using sets, and by giving legitimacy to non-Euclidean spatial geometry, it will open the possibility of future research.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.121-134
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• 2011

Stevin is known as the inventor of decimal fractions, even though many mathematicians had the concept of decimal fractions and used it before Stevin. Why? To respond to such a question, we studied about its significance which 'La Disme' had in the history of mathematics. These can be summarized as its notational aspect, the manner of developing the book, the conceptual revolution and the practical purpose. And the chapter and verse of are little known when compared to its reputation. So in this paper we considered its contents in detail and discussed some didactical implications in relation to teaching and learning of decimal fractions in elementary school : importance of place values, similarity of calculation to natural numbers, using common fractions to justify, emphasis on the applications of decimal fractions, relation to measuring units, necessity of teaching number sense, using notational aspects.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.273-287
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• 2018

The purpose of this study was to analyze changing aspect of teacher and student's value in mathematics instruction. For this purpose, teacher and student's value are analyzed through value questionnaire by four times. The results of this study revealed that although value are individual's deep decision mechanism, it could change considerably by the time. Teacher wasn't compel students to follow her value. Rather, teacher was modified instruction goal to reflect students thinking what is important in mathematics lesson. First, in case of mathematical value, rationalism, objectism, mystery were convergent each other. And control was almost unchanged and openness has been onwards and upwards. Second, in case of mathematics educational value, understanding, pleasure, terminology and application were convergent each other. However achievement was almost unchanged. Also, to teach effectively, teacher using several kinds strategy while negotiate with student's value continuously. On the basis of these results, this paper includes several implications for the future study about values in mathematics which could be the critical factor in student centered instruction.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.467-490
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• 2013

Correlation is a basic statistical concept which is necessary for understanding the relationship between two variables when they change values. In the middle school curriculum of Korea, only informal definition of correlation is taught with two-way data representations such as scatter plots and contingency tables. In this study, we investigated Korean high school students' understanding of correlation using a test consisting of 35 items about interpretation of scatter plot, contingency table, and text in realistic situation. 216 students from a high school in Seoul took the test for 20 minutes. From the results, we could observe the following: First, students did not have right criteria for determining the strength of correlation presented in scatter plots. Most of students could determine if there is correlation/no correlation and if the correlation is positive/negative by seeing the data presented in scatter plots. However, they did not judge by the closeness to the regression line but rather judged by the closeness between data points. Second, when statements about comparing the strength of correlation in the context of real life situation were given in text, the students had difficulty in understanding the distribution-related characteristic of the bi-variate data. Students had difficulty in figuring out the local distribution characteristic of data, which cannot be guessed merely based on the expression 'The correlation is strong' without statistical knowledge of correlation. Third, a large number of students could not judge the association between two variabels using conditional proportions when qualitative data are given in 2-by-2 tables. They made judgement by the absolute cell count and when the marginal sum of two categories are different for explanatory variable they thought the association could not be determined. From these results, we concluded that educational measures are required in order to remove such misconceptions and to improve understanding of correlation. Considering that the current mathematics curriculum does not cover the concept of correlation, we need to improve the curriculum as well.

• School Mathematics
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• v.19 no.2
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• pp.345-367
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• 2017

The purpose of this study is to investigate the proportional reasoning of middle school students during the process of expressing and interpreting the graphs. We collected data from a teaching experiment with four 7th grade students who participated in 23 teaching episodes. For this study, the differences between student A and student B-who joined theteaching experiment from the $1^{st}$ teaching episode through the $8^{th}$ -in understanding graphs are compared and the reason for their differences are discussed. The results showed different proportional solving strategies between the two students, which revealed in the course of adjusting values of two given variables to seek new values; student B, due to a limited ability for proportional reasoning, had difficulty in constructing graphs for given situations and interpreting given graphs.

• Journal of the Korea Convergence Society
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• v.9 no.10
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• pp.217-228
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• 2018

The purpose of this study is to develop STEAM program for gifted education by combining educational contents of humanities, arts, engineering, technology, and design into various subjects, focusing on mathematics-science curriculum of elementary school. The achievement standards and curriculum contents of elementary mathematics-science curriculum were analyzed while considering 2015 revised national curriculum. And then, a 16 class-hour convergence education program consisting of 3-hour block time was developed by applying the STEAM model with 4 steps. The validity of the program developed through this process was verified, and four educational experts evaluate whether the program can be applied to the elementary school. Based on the evaluation results, the convergence education program was finalized. As a result of implementing the gifted education program for mathematics-science, students achieved the objectives and values of convergence education such as creative design, self-directed participation, cooperative learning, and interest in class activities (game, making). If this convergence education program is applied to regular class, creative experiential class, or class for gifted children, students can promote their scientific creativity, artistic sensitivity, design sence, and so on.

• School Mathematics
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• v.15 no.1
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• pp.159-177
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• 2013

This study is a case study of STEAM education. We have developed teaching and learning materials, suggested teaching method, and analysed the result for exploring the potential and effect of STEAM. The content of this study is based on the history of mathematics. Science (S) is related to the 24 divisions of the year, the height of the sun, the movement of heavenly bodies. Technology (T) is related to the exploration with graphic calculators. Engineering (E) is related to design sundial and research on the design principles. Art (A) is related to literature review about mathematical history, the understanding of the value of the mathematics. Mathematics (M) is related to the trigonometric functions. We have considered that Project-Based Learning is proper teaching and learning for STEAM education, we have designed the STEAM PBL and analysed the results focused on the developing integrative knowledge, mathematical attitude including mathematical value, the competencies of 21 century. The result of this study is as follows. We find that STEAM education activates students' collaboration, communication skills and improves representation and critical thinking skills. Also STEAM education makes positive changes of students' mathematical attitudes including the values of the mathematics.

• Journal for History of Mathematics
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• v.31 no.2
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• pp.73-91
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• 2018

This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.